Speaking in an interview with DJ Gary Crowley on BBC radio station London Live 94.9FM, which will be broadcast as a two-hour documentary special on May 8, McCartney said that as a teenager one of his great ambitions was to write a song for Sinatra.

He said: “When I was about 14, we were looking at this idea of becoming composers. And the ambition then was to write for Frank Sinatra. That was the height a writer would aspire to. That would have been the epitome, we just grew up with that idea.

“I had written [a song] in my teen years, and would always play it as my party piece… it went on and got a bit disastrous as it went on, the lyrics got very bad… it ended with ‘It’s suicide’. And the title was ‘It’s Suicide’.”

McCartney sent the demo to Sinatra, who was unimpressed. He continued: “I sent this demo with me singing it, and apparently he [Sinatra] said, ‘Is this guy taking the piss? What is this?’… Unfortunately he didn’t like the song, I still think it would have been good… Lyrically unsound, but I could have fixed it, Frank!”

McCartney has recently compiled a Wings anthology, titled ‘Wingspan’, released in May. Following the promotional duties for that record, he plans to release a new album.

He said: “I want to finish a new album of new songs, I’m pretty excited about that. I got hooked up with some American producer, and he put me with three players I had never met – it was great, we just went on fire. Sometime in late September there may be a new album.”